Mode-locked solid-state laser apparatus

ABSTRACT

In a mode-locked laser-diode-excited laser apparatus: a solid-state laser medium is arranged at a distance of at most twice the Rayleigh range from a saturable absorbing mirror with a depth of absorbing modulation of at least 0.4%; the total intracavity dispersion is smaller than zero and makes oscillating light have such a pulse bandwidth that the saturable absorbing mirror can suppress a background pulses other than soliton pulses repeated with a fundamental repetition period, and the magnitude of the total intracavity dispersion has a predetermined relationship with a pulse width of the oscillating light; and an output mirror is a negative-dispersion mirror being constituted by two multilayer mirrors and a cavity layer sandwiched between the two multilayer mirrors, and causing a mirror dispersion of −3000 fsec 2  to −600 fsec 2  and realizes a reflectance of 97% to 99.5%.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a solid-state laser apparatus, and inparticular to a small-sized, mode-locked solid-state laser apparatuswhich has high output power, and enables highly efficient, short-pulsegeneration.

2. Description of the Related Art

Conventionally, efforts of developing solid-state lasers in which asolid-state laser medium (e.g., a laser crystal, ceramic substance,glass, or the like) doped with rare-earth ions or transition-metal ionsis excited with a semiconductor laser (laser diode (LD)) as anexcitation light source have been actively made. Among others, a widevariety of applications of the short-pulse lasers, which emit theso-called short light pulses (having the durations on the order ofpicoseconds to femtoseconds), have been searched for and proposed, andpart of such applications have been put into practical use afterverification.

In the short-pulse lasers, the short light pulses are generated by anoperation called mode locking. The mode locking is a technique of makinga great number of longitudinal-mode laser oscillations in phase (i.e.,making the phase differences between the longitudinal-mode laseroscillations zero) so as to produce pulses having very small durationsin the time domain by multimode interference between thelongitudinal-mode laser oscillations. In particular, for the solid-statelasers, the mode locking using the semiconductor saturable absorbingmirror (SESAM) is advantageous since the SESAM can realize solid-statelasers which are simple in structure, low in cost, and small in size,and the mode locking automatically starts in the solid-state lasersusing the SESAM. Therefore, efforts of studying and developing the modelocking using the SESAM have been vigorously made.

Especially, the soliton mode locking, which is a type of mode locking,enables generation of pulses having the durations on the order offemtoseconds by a combination of negative group-velocity dispersion inthe laser resonator and self-phase modulation, which mainly occurs inthe laser medium. More specifically, in the soliton mode locking, theSESAM starts the mode locking and maintains and stabilizes generation ofpulses, and the negative group velocity dispersion and the self-phasemodulation are balanced so as to produce soliton pulses and steepen themode-locked pulses. Thus, the soliton mode locking enables stable pulsegeneration. (The soliton mode locking is defined, for example, in F.Brunner et al., “Diode-pumped femtosecond Yb:KGd(WO₄)₂ laser with 1.1-Waverage power”, Optics Letters, Vol. 25, No. 15, pp. 1119-1121, 2000,and C. Hönninger et al., “Q-switching stability limits ofcontinuous-wave passive mode locking”, Journal of the Optical Society ofAmerica B, Vol. 16, No. 1, pp. 46-56, 1999.)

The solid-state laser apparatus realizing the soliton mode locking isbasically configured by arranging in a resonator a solid-state lasermedium, a saturable absorbing mirror, and a negative dispersion element(negative group-velocity dispersion element).

FIG. 19 illustrates a typical configuration of a conventionalmode-locked, Yb-doped solid-state laser, which is disclosed in theBrunner reference, where the solid-state laser medium is Yb:KGd(WO₄)₂.In FIG. 19, reference number 80 denotes a pair of excitation lightsources, 81 denotes a pair of input optical systems, 83 denotes asolid-state laser medium, M₁ and M₂ denote a pair of concave mirrors, 84denotes a concave mirror, 85 denotes an SESAM, 86 and 87 denote a pairof prisms, 88 denotes knife-edge plates, and 89 denotes an outputcoupler. The pair of excitation light sources 80 emit excitation lighthaving the wavelength of, for example, 980 nm. The input optical systems81 are respectively arranged in association with the excitation lightsources 80. The concave mirrors M₁ and M₂ have a curvature radius of,for example, 20 cm, and constitute a resonator. The concave mirror 84has a curvature radius of 20 cm. The prisms 86 and 87 are made of, forexample, SF10 glass. The output coupler 89 has a transmittance of, forexample, 4.3%.

Generally, in the mode-locked solid-state laser apparatuses having aconfiguration as above, the beam in resonator is condensed by each ofthe concave mirrors M₁, M₂, and 84 in order to reduce the spot size(i.e., the mode radius ω_(L)) of the oscillating light in the lasermedium and the spot size (i.e., the mode radius ω_(A)) at the SESAM. Thespot sizes in the laser medium and the SESAM are reduced for the firstpurpose of lowering the threshold for laser oscillation (laseroscillation threshold) and the second purpose of satisfying a conditionfor soliton mode locking.

The first purpose (of lowering the laser oscillation threshold) isexplained below.

The laser oscillation threshold P_(th) is expressed by the formula,

$\begin{matrix}{P_{th} = {\frac{\pi \; h\; {\nu_{P}( {\omega_{L}^{2} + \omega_{P}^{2}} )}}{4\; \sigma \; \tau \; {\eta_{a}( {f_{1} + f_{2}} )}}( {L_{1} + T_{OC} + {2f_{1}\sigma \; N_{0}l_{S}}} )}} & (1)\end{matrix}$

where ω_(L) is the beam radius of the oscillating light in thesolid-state laser medium, ω_(P) is the beam radius of the excitationlight in the solid-state laser medium, hν_(p) is the photon energy ofthe excitation light, σ is the stimulated-emission cross section of thesolid-state laser medium, τ is the lifetime of the upper level, η_(a) isthe absorption efficiency, f₁ is the filling factor of the lower level,f₂ is the filling factor of the upper level, L₁ is the internal loss ofthe resonator, T_(0C) is the transmittance of the output mirror, N₀ isthe doping concentration of the rare-earth ions, and l_(S) is thecrystal length. (See T. Taira et al., “Modeling of quasi-three-levellasers and operation of cw Yb:YAG lasers”, Applied Optics, Vol. 36, No.9, pp. 1867-1874, 1997.)

It is possible to understand, on the basis of the formula (1), that thelaser oscillation threshold can be lowered by reducing the beam radiusω_(P) of the excitation light and the radius ω_(L) of the oscillatinglight in the solid-state laser medium.

The Hönninger reference reports that a Q-switching operation is mixed inthe mode locking operation (i.e., a Q-switched mode locking occurs)under a certain condition in a soliton-mode-locked laser. When theQ-switched mode locking occurs, mode-locked pulses (having a frequencyof 10 MHz to 1 GHz and a width on the order of picoseconds tofemtoseconds) are superimposed on long Q-switched pulses (having afrequency of 1 kHz to 100 kHz and a width on the order of microsecondsto nanoseconds). However, generally, the Q-switched mode locking isundesirable in the applications other than the energetic use because ofthe instability in the output, pulse width, and pulse period. Accordingto the Hönninger reference, a condition for preventing the Q-switchingoperation during the soliton mode locking by use of the saturableabsorbing mirror can be expressed by the inequality,

F _(sat,L) ·A _(eff,L) ·g·K ² E _(P) ³ +E _(P) ² >F _(sat,L) ·A _(eff,L)·F _(sat,A) ·A _(eff,A) ·ΔR,   (2)

where E_(P) is the pulse energy inside the resonator, ΔR is the depth ofthe absorbing modulation in the saturable absorbing mirror, F_(sat,A) isthe saturation fluence in the saturable absorbing mirror,F_(sat,L)(=hν/σ) is the saturation fluence in the laser medium, hν isthe photon energy of the laser light, A_(eff,A)(=πω_(A) ²) is theoscillated-light-beam cross section at the saturable absorbing mirror,A_(eff,L)(=πω_(L) ²) is the oscillated-light-beam cross section in thelaser medium, and g is the laser gain in the laser medium. The factor Kin the inequality (2) can be expressed as,

$\begin{matrix}{K = {\frac{4\; \pi \; n_{2}l_{S}}{{D}A_{{eff},L}\lambda_{0}\Delta \; \nu_{G}}\frac{0.315}{1.76}}} & (3)\end{matrix}$

where n₂ is the nonlinear refractive index of the laser medium, D is thegroup-velocity dispersion (D<0) occurring in a round trip in the entireresonator, λ₀ is the central wavelength of the oscillating light, andΔν_(G) is the gain bandwidth. It is known that the so-called CW(continuous-wave) mode locking, which is free from Q-switchinginstability, is realized when the pulse energy E_(P) satisfying thecondition expressed by the inequality (2) is satisfied in a resonator byreducing the oscillated-beam cross sections A_(eff,A) and A_(eff,L). Themode-locking threshold value can be obtained as a solution E_(P) of anequation expressed by replacing the inequality sign in the inequality(2) with an equal sign. In other words, when the pulse energy E_(P)inside the resonator exceeds the mode-locking threshold value, theinequality (2) is satisfied.

The two conditions for the laser oscillation threshold and the (CW)mode-locking threshold value which are explained above require reductionof the oscillated-beam cross sections A_(eff,A) and A_(eff,L) in thelaser medium and the SESAM. In many of the conventional mode-lockedsolid-state lasers, a pair of concave mirrors are arranged on both sidesof the laser medium and near the SESAM so as to condense the beam. (Inthe example of FIG. 19, the curvature radii of the concave mirrors M₁and M₂ are normally 100 to 200 nm.)

Normally, the concave mirrors M₁ and M₂ on both sides of the lasermedium 83 are arranged at distances approximately halves of thecurvature radii of the concave mirrors M₁ and M₂ from the laser medium83, and the concave mirror 84 near the SESAM 85 is arranged at adistance approximately half of the curvature radius of the concavemirror 84 from the SESAM 85. Therefore, when the curvature radii of theconcave mirrors are 100 to 200 mm, the necessary dimensions of the partof the solid-state laser containing the concave mirrors M₁ and M₂ andthe laser medium 83 and the part of the solid-state laser containing theconcave mirror 84 and the SESAM 85 are approximately 150 to 300 mm.Thus, in consideration of the spaces for arrangement of the othercomponents such as the negative dispersion elements, the necessarylength of the resonator becomes approximately 500 to 1000 mm. That is,the size of the solid-state laser apparatus becomes large. In theconfiguration of FIG. 19, the pair of prisms 86 and 87, which aredistanced by 450 mm, cause negative dispersion. However, generally,solid-state laser apparatuses containing a one-meter class resonator arehard to stably operate. Therefore, the stability of the laseroscillation in the conventional solid-state laser apparatuses is low. Inaddition, since the conventional solid-state laser apparatuses areconstituted by a great number of optical components, the cost of theconventional solid-state laser apparatuses is high.

In the above circumstances, downsizing of the mode-locked solid-statelaser apparatuses is demanded for increasing the stability of the laseroscillation.

U.S. Pat. No. 7,106,764 (hereinafter referred to as U.S. Pat. No.7,106,764) proposes a small-sized solid-state laser apparatus 100 asillustrated in FIG. 20. In the solid-state laser apparatus 100, aresonator is constituted by a solid-state laser medium 101 and a SESAM102. The solid-state laser medium 101 and the SESAM 102 are arrangedthrough a ring 108 so that a predetermined gap 103 is produced betweenthe solid-state laser medium 101 and the SESAM 102. The gap 103 has thefunction of a GTI (Gires-Tournois interferometer) and causes negativedispersion. An end surface 104 of the laser medium 101 is a curvedsurface, and is coated so as to behave as an output mirror 105.Excitation light 106 is inputted and output light 107 is outputtedthrough the output mirror 105.

Japanese Unexamined Patent Publication No. 11(1999)-168252 (hereinafterreferred to as JP11-168252A) proposes provision of a chirped-mirrorcoating (negative-dispersion coating) on a laser medium, a saturableabsorbing mirror, or an output mirror. For example, JP11-168252Aproposes a small-sized laser apparatus 110 as illustrated in FIG. 21. Inthe laser apparatus 110, a saturable absorbing mirror 112 is formed onan end surface of a laser medium 111 by coating, so that a resonator isformed between the saturable absorbing mirror 112 and a chirped mirror113, which is a negative-dispersion mirror. Excitation light 115 isgenerated by a semiconductor laser 114 and inputted into the lasermedium 111, and output light 116 is outputted through the chirped mirror113.

As explained above, U.S. Pat. No. 7,106,764 proposes downsizing of asolid-state laser apparatus by close arrangement of the solid-statelaser medium and the SESAM, and JP11-168252A proposes downsizing of asolid-state laser apparatus by reduction of the number of opticalcomponents. In JP11-168252A, the number of optical components is reducedby producing the saturable absorbing mirror 112 by coating on thesolid-state laser medium, and arranging the solid-state laser apparatusso that the negative-dispersion mirror is also used as the outputmirror.

Although, generally, one or a combination of a pair of prisms, a pair ofdiffraction gratings, a negative-dispersion mirror, and the like is usedas the negative dispersion element, the configuration in which thenegative-dispersion mirror is also used as the output mirror (asdisclosed in JP11-168252A) is desirable from the viewpoint ofdownsizing.

The chirped mirror and the GTI mirror are known to be anegative-dispersion mirror. For example, JP11-168252A discloses achirped mirror which makes negative dispersion compensation(compensation with a negative dispersion) by taking advantage of thedifference in light penetration between the longer wavelengths andshorter wavelengths. The GTI mirror makes negative dispersioncompensation by taking advantage of optical interference occurringbetween a total-reflection mirror and a partial-reflection mirror.

In a typical example of the chirped mirror, high-index layers havingrelatively high refractive indexes and low-index layers havingrelatively low refractive indexes are alternately laminated in such amanner that the optical thicknesses of the high-index layers and theoptical thicknesses of the low-index layers linearly vary along thethickness direction. (See, for example, R. Szipocs et al., “Chirpedmultilayer coatings for broadband dispersion control in femtosecondlasers”, Optics Letters, Vol. 19, No. 3, pp. 201-203, 1994.)

On the other hand, the GTI mirror is characterized by having a resonantstructure inside a dielectric multilayer film. (See, for example, J.Kuhl and J. Heppner, “Compression of Femtosecond Optical pulses withDielectric Multilayer Interferometers”, IEEE Transaction on QuantumElectronics, Vol. QE-22, No. 1, pp. 182-185, 1986.) In addition, a GTImirror having a double-GTI structure with two cavity layers arrangedinside a multilayer film (as disclosed in U.S. Pat. No. 6,081,379(hereinafter referred to as U.S. Pat. No. 6,081,379)) and a GTI mirrorhaving a resonant structure in which no cavity layer is arranged and theoptical thicknesses of multiple layers constituting a multilayer filmvary in accordance with a certain rule (as disclosed in InternationalPatent Publication No. WO00/11501 (hereinafter referred to asWP0011501A1)) have been proposed.

Further, Japanese Unexamined Patent Publication No. 2(1990)-023302(hereinafter referred to as JP2-023302A) proposes a dielectricmultilayer-film stack which compensates for the third- or higher-orderdispersion as well as the second-order dispersion. The dielectricmultilayer-film stack is formed by stacking two or more dielectricmultilayer films in which two or more index layers having differentrefractive indexes are alternately laminated, and the dielectricmultilayer films have respectively different central frequencies.Japanese Unexamined Patent Publication No. 2000-138407 (hereinafterreferred to as JP2000-138407A) proposes a multilayer mirror in which theoutermost layers have refractive indexes respectively lower than thelayers immediately below the outermost layers, and which exhibits areflectance of 95% or higher in the visible wavelength range and causesnegative group-velocity dispersion.

As explained above, in order to realize downsizing of a mode-lockedsolid-state laser apparatus, it is possible to consider the closearrangement of the solid-state laser medium and the SESAM and the use ofthe negative-dispersion mirror as an output mirror.

However, the conventional techniques explained above have the followingproblems.

(a) Although JP11-168252A proposes the use of the negative-dispersionmirror as the output mirror, and the negative-dispersion mirror isproduced by chirped-mirror coating (having a negative dispersionfunction), JP11-168252A does not concretely disclose details of thenegative-dispersion mirror (such as the optical transmittance, theamount of dispersion, the dielectric films constituting thenegative-dispersion mirror, and the like) for use as the output mirror.That is, JP11-168252A does not disclose information necessary forrealizing the negative-dispersion mirror which is produced bychirped-mirror coating and can be used as the output mirror.

(b) Although JP2000-138407A reports that the frequency chirp can becompensated for by arranging a dielectric multilayer film on the outputmirror, the reflectance of the dielectric multilayer film disclosed inJP2000-138407A is 99.9% or higher, i.e., approximately 100%. That is,almost no output light can be outputted through such an output mirror.Therefore, the dielectric multilayer film disclosed in JP2000-138407Adoes not have a sufficient function of an output mirror.

(c) Since the magnitudes of negative dispersion caused by thecommercially available negative dispersion elements are tens to hundredsof square femtoseconds, it is necessary to arrange more than onenegative dispersion element in the resonator for making sufficientnegative dispersion compensation. Therefore, it is difficult to achievesatisfactory downsizing and stabilization of the solid-state laserapparatus.

(d) The solid-state laser apparatuses in which the saturable absorbingmirror (as a reflection mirror) is arranged in close vicinity to or incontact with the laser medium as disclosed in U.S. Pat. No. 7,106,764 orJP11-168252A have the following problems.

As indicated in R. Paschotta et al., “Passive mode locking of thin-disklasers: effects of spatial hole burning”, Applied Physics B, Vol. 72,No. 3, pp. 267-278, 2001, B. Braun et al., “Continuous-wave mode-lockedsolid-state lasers with enhanced spatial holeburning”, Applied PhysicsB, Vol. 61, No. 5, pp. 429-437, 1995, and F. X. Kärtner et al.,“Continuous-wave mode-locked solid-state lasers with enhanced spatialhole burning”, Applied Physics B, Vol. 61, No. 6, pp. 569-579, 1995, itis known that the spatial hole burning differently occurs in the lasermedium (as the gain medium) according to the position along the opticalaxis, is coupled to the mode locking phenomenon, and affects thestability of the mode locking.

The phase of the electric field of the optical wave jumps at thereflection mirror surfaces of the resonator, and nodes of the electricfield (at which the electric field strength is zero) exist at thereflection mirror surfaces. In the case where the laser medium isarranged in close vicinity of a reflection mirror surface, the intensityof the laser wave has a stripe-like spatial distribution in the lasermedium because of the phase jump at the reflection mirror surface. Thisphenomenon is the spatial hole burning.

The Paschotta reference reports that in the case where the laser mediumis arranged in close vicinity of a reflection mirror, a dip is producedin a gain spectrum, and makes the soliton pulses traveling between thereflection surfaces in the resonator unstable. Specifically, since thehole burning effect is relatively strongly manifested in the vicinity ofthe reflection mirror, the gain spectrum (in the frequency domain) ofthe laser pulses traveling between the reflection surfaces in theresonator (which are soliton pulses having a relatively wide bandwidth)is also affected, and the gain is preferentially imparted to undesirablephenomena (such as generation of shifted pulses, double pulses, andcontinuous background) competing the desired pulses. Therefore, thedesired soliton pulses lose in the competition, and the aboveundesirable phenomena make the operation of the solid-state laserapparatus unstable. Consequently, in the case where the saturableabsorbing mirror (as a reflection mirror) is arranged in close vicinityto or in contact with the laser medium as disclosed in U.S. Pat. No.7,106,764 or JP11-168252A, it is possible to consider that the spatialhole burning conspicuously occurs, and the generation of soliton pulsesbecomes extremely unstable. However, neither U.S. Pat. No. 7,106,764 norJP11-168252A mentions the influence of the spatial hole burning on themode stability, and teaches a means for realizing the mode stability.

As explained above, various proposals for downsizing of the mode-lockedsolid-state laser apparatuses have been conventionally made, nocondition for stably generating soliton pulses in downsized solid-statelaser apparatuses has been definitely proposed. In addition, nonegative-dispersion mirror which can make sufficient negative dispersioncompensation by itself and can also operate as an output mirror has beenreported. That is, no small-sized, mode-locked solid-state laserapparatus which satisfactorily operates has been conventionallyrealized.

SUMMARY OF THE INVENTION

The present invention has been developed in view of the abovecircumstances.

The object of the present invention is to provide a small-sized,mode-locked solid-state laser apparatus which can be manufactured at lowcost, can stably operate, and can realize continuous-wave (CW) modelocking.

In order to accomplish the above object, the present invention isprovided. According to the present invention, there is provided amode-locked solid-state laser apparatus comprising: a resonator havingan output mirror at one end of the resonator; a solid-state laser mediumarranged in the resonator; and a saturable absorbing mirror. Thesolid-state laser medium is arranged at a distance equal to or smallerthan twice the Rayleigh range from the saturable absorbing mirror; thesaturable absorbing mirror has a depth of absorbing modulation equal toor greater than 0.4%; the mode-locked solid-state laser apparatus isconfigured to impart a total intracavity dispersion D to light having apredetermined wavelength during a round trip of the light in theresonator, where the total intracavity dispersion D is smaller than zeroand makes the light have such a pulse bandwidth that the saturableabsorbing mirror can suppress operational modes other than operationalmodes generating soliton pulses repeated with a fundamental repetitionperiod, and the absolute value |D| of the total intracavity dispersion Dhas a relationship expressed by the equation,

$\begin{matrix}{{\tau_{P} = {\frac{1.76{D}\lambda_{0}A_{{eff},L}}{4\; \pi \; n_{2}l_{S}}\frac{1}{E_{P}}}},} & (4)\end{matrix}$

with a pulse width τ_(P) and a central wavelength λ₀ of the light, abeam cross section A_(eff,L) of the light in the solid-state lasermedium, a nonlinear refractive index n₂ and a crystal length l_(S) ofthe solid-state laser medium, pulse energy Ep in the resonator; theoutput mirror is a negative-dispersion mirror which has a dielectricmultilayer structure being formed on a substrate and including twomultilayer mirrors and a cavity layer, which is sandwiched between thetwo multilayer mirrors and causes resonance of the light between the twomultilayer mirrors; and the negative-dispersion mirror causes a mirrordispersion of −3000 fsec² to −600 fsec² (i.e., equal to or greater than−3000 fsec² and equal to or smaller than −600 fsec²) in the light havingthe predetermined wavelength and realizes a reflectance of 97% to 99.5%(i.e., equal to or greater than 97% and equal to or smaller than 99.5%)at the predetermined wavelength. The beam cross section A_(eff,L) of thelight in the solid-state laser medium can be expressed as πω_(L) ²,where ω_(L) is the radius of the beam of the light in the solid-statelaser medium.

The present inventors have made investigations on downsizing ofmode-locked solid-state laser apparatuses, and found that mode-lockedsoliton pulses can be generated by arranging a laser medium at adistance not exceeding twice the Rayleigh range from an SESAM even inconfigurations in which the beam waist is not formed in the lasermedium.

In addition, the present inventors have also found that certainlimitations should be imposed on the depth of absorbing modulation inthe saturable absorbing mirror and the total dispersion in the resonatorin order to stabilize the mode-locked operations in small-sizedmode-locked solid-state laser apparatuses, and the present inventorshave clearly indicated the limitations. That is, the limitations on thedepth ΔR of absorbing modulation in the saturable absorbing mirror andthe total intracavity dispersion D caused in the light during a roundtrip of the light in the resonator (which is hereinafter referred to asthe total intracavity dispersion D) have been found as a result of closeinvestigation on the stability of the mode locking.

Further, the present inventors have found that in order to use anegative-dispersion mirror as an output mirror (or use an output mirroras a negative-dispersion mirror) for the downsizing of a mode-lockedsolid-state laser apparatus, the negative-dispersion mirror is requiredto have such a reflectance as to allow output of laser pulses, and isalso required to cause such a total intracavity dispersion to realizestable operation.

The Rayleigh range is a quantity defined as z_(R)=πω_(A) ²/λ, and is thedistance along the optical axis from the beam waist to a location atwhich the radius of the beam of the oscillating light is √2 times theradius ω_(A) at the beam waist. In addition, the condition that “thesolid-state laser medium is arranged at a distance equal to or smallerthan twice the Rayleigh range from the saturable absorbing mirror”allows the arrangement in which the distance is zero, i.e., thesaturable absorbing mirror may be arranged in contact with thesolid-state laser medium. Further, the “operational modes other thanoperational modes which generate soliton pulses repeated with afundamental repetition period” means, for example, the modes ofoperation in which pulses (such as double pulses, continuous-wavebackground, and the like) competing with the fundamental soliton pulsesrepeated with the fundamental repetition period are generated asillustrated in FIG. 2.

TABLE 1 Pulse Energy Pulse Central (Arbitrary Bandwidth Frequency Unit)(Frequency) Soliton Pulse ν₀ 1 Δν_(p) Frequency-shifted ν₀-δν_(shift) 1Δν_(p) Pulse CW Background ν₀-δν_(CW) — Narrow Bandwidth Double Pulseν₀-δν_(double) ½ Δν_(p)/2

FIG. 2 illustrates examples of spectra (in the frequency domain) and thewaveshapes of the fundamental soliton pulses repeated with thefundamental repetition period, the frequency-shifted pulses, the doublepulses, and the continuous-wave (CW) background, and Table 1 indicatesthe central frequencies, pulse energies, and pulse bandwidths of thesoliton pulses repeated with the fundamental repetition period, thefrequency-shifted pulses, the CW background, and the double pulses. Thefrequency-shifted pulses with which the soliton pulses repeated with thefundamental repetition period compete have a central frequency which isshifted by δν_(shift) from the central frequency of the soliton pulsesrepeated with the fundamental repetition period, although thefrequency-shifted pulses have the same pulse bandwidth and pulse energyas the soliton pulses. The CW background with which the soliton pulsesrepeated with the fundamental repetition period compete is acontinuous-wave component which does not have a pulse-like waveshape inthe time domain, and has a very narrow bandwidth in the frequencydomain. The double pulses with which the soliton pulses repeated withthe fundamental repetition period compete are a series of pulses thepulse energies of which are halves of the pulse energy of the solitonpulses repeated with the fundamental repetition period, and the pulsebandwidths of which are half of the pulse bandwidth of the solitonpulses repeated with the fundamental repetition period. Although nofrequency shift from the soliton pulses repeated with the fundamentalrepetition period is illustrated in the spectra for the double pulsesand the CW background in FIG. 2 for simple illustration, actually, thefrequencies of the double pulses and the CW background are shifted fromthe soliton pulses repeated with the fundamental repetition period.

Although the aforementioned “operational modes other than operationalmodes which generate soliton pulses repeated with a fundamentalrepetition period” according to the present invention include theoperational modes in which the double pulses and the CW background aregenerated, the “operational modes other than operational modes whichgenerate soliton pulses repeated with a fundamental repetition period”according to the present invention do not include the operational modesin which the frequency-shifted pulses are generated, since thefrequency-shifted pulses cannot be suppressed by control of the depth ofabsorbing modulation.

Although the total intracavity dispersion D has the relationshipexpressed by the equation (4) with the pulse width τ_(P) (which isinversely proportional to the pulse bandwidth) and the other parameters,the total intracavity dispersion D is set to a value in a range which isdetermined on the basis of such a pulse bandwidth that the pulses (suchas the double pulses and the CW background) generated by the spatialhole burning in competition with the desired soliton pulses can besuppressed with the depth of absorbing modulation at the saturableabsorbing mirror which is set to a value equal to or greater than 0.4%.

Preferably, the solid-state laser apparatus according to the presentinvention may also have one or any possible combination of the followingadditional features (i) to (xxii).

(i) It is preferable that the resonator include a dichroic mirror whichtransmits the light and is arranged on the optical axis or on anextension of the optical axis so that when excitation light for excitingthe solid-state laser medium is injected into the resonator along adirection nonparallel to the optical axis, the excitation light isreflected by the dichroic mirror and propagates along the optical axis.For example, the excitation light may be injected into the resonatoralong a direction perpendicular to the optical axis.

(ii) It is preferable that the solid-state laser medium be doped with arare-earth element. In this case, the rare-earth element may be at leastone of ytterbium (Yb), erbium (Er), and neodymium (Nd), and thesolid-state laser medium may be one of Yb:YAG (Y₃Al₅O₁₂), Yb:KYW(KY(WO₄)₂), Yb:KGW (KGd(WO₄)₂), Yb:Y₂O₃, Yb:Sc₂O₃, Yb:Lu₂O₃,Er,Yb:glass, and Nd:glass.

(iii) It is preferable that the resonator be a linear resonator.

(iv) It is preferable that the light have a mode diameter of 100micrometers or smaller at the beam waist when the light is oscillated inthe resonator. In this specification, the diameter of a beam is definedas the diameter of the beam spread in a cross section perpendicular tothe light propagation direction within which the intensity of the beamis 1/e² or more of the peak intensity.

(v) In the case where the solid-state laser medium is Yb:KYW, it ispreferable that the total intracavity dispersion D be equal to orgreater than −2500 fsec² and smaller than 0 fsec².

(vi) In the case where the solid-state laser medium is Yb:KGW, it ispreferable that the total intracavity dispersion D be equal to orgreater than −5750 fsec² and smaller than 0 fsec².

(vii) In the case where the solid-state laser medium is Yb:YAG, it ispreferable that the total intracavity dispersion D be equal to orgreater than −1750 fsec² and smaller than 0 fsec².

(viii) In the case where the solid-state laser medium is Yb:Y₂O₃, it ispreferable that the total intracavity dispersion D be equal to orgreater than −3250 fsec² and smaller than 0 fsec².

(ix) In the case where the solid-state laser medium is Yb:Lu₂O₃, it ispreferable that the total intracavity dispersion D be equal to orgreater than −3000 fsec² and smaller than 0 fsec².

(x) In the case where the solid-state laser medium is Yb: Sc₂O₃, it ispreferable that the total intracavity dispersion D be equal to orgreater than −3000 fsec² and smaller than 0 fsec².

(xi) In the case where the solid-state laser medium is Er,Yb:glass, itis preferable that the total intracavity dispersion D be equal to orgreater than −1200 fsec² and smaller than 0 fsec².

(xii) The preferable range of the total intracavity dispersion D isdifferent according to the solid-state laser medium. On the other hand,the laser crystal arranged in the resonator and various coatings cangenerally impart a positive group-velocity dispersion to the light. Evenin the case where the number of components in the resonator isminimized, the positive dispersion of +100 fsec² to +500 fsec² isimparted in total. Therefore, a negative-dispersion mirror which causesa (mirror) dispersion of −3000 fsec² to −600 fsec² can be preferablyused. In addition, a quartz substrate or the like which imparts adesired positive dispersion may be inserted in a resonator, whennecessary, so as to achieve the desired amount of the total intracavitydispersion D according to the solid-state laser medium.

(xiii) The length of the resonator in the mode-locked solid-state laserapparatus according to the present invention is preferably equal to orsmaller than 200 mm, more preferably equal to or smaller than 100 mm,further preferably equal to or smaller than 75 mm, and yet furtherpreferably equal to or smaller than 50 mm.

(xiv) It is preferable that the substrate of the negative-dispersionmirror have a concave surface, and the dielectric multilayer structurebe arranged at the concave surface.

(xv) It is preferable that the negative-dispersion mirror cause themirror dispersion of −3000 fsec² to −600 fsec² and realizes thereflectance of 97% to 99.5% in a wavelength range containing thepredetermined wavelength and having a bandwidth equal to or greater than10 nm.

(xvi) It is preferable that the predetermined wavelength be in awavelength range of 1000 nm to 1100 nm.

(xvii) It is preferable that the cavity layer in the negative-dispersionmirror have an optical thickness equal to or greater than half of thepredetermined wavelength. In addition, it is preferable that the opticalthickness of the cavity layer in the negative-dispersion mirror be atmost approximately ten times the predetermined wavelength. Further, itis particularly preferable that the optical thickness of the cavitylayer in the negative-dispersion mirror be approximately twice to fourtimes the predetermined wavelength.

(xviii) It is preferable that each of layers constituting the twomultilayer mirrors in the negative-dispersion mirror have an opticalthickness equal to or greater than one-eighth of the predeterminedwavelength and smaller than half of the predetermined wavelength.

(xix) It is preferable that each of the two multilayer mirrors in thenegative-dispersion mirror be constituted by high-index layers havingrelatively high refractive indexes and low-index layers havingrelatively low refractive indexes which are alternately laminated, andthe total number of the high-index layers and the low-index layers ineach of the two multilayer mirrors be eight or greater.

(xx) In the mode-locked solid-state laser apparatus having the feature(xix), it is preferable that the cavity layer in the negative-dispersionmirror be formed of an identical material to one of the high-indexlayers and the low-index layers.

(xxi) In the mode-locked solid-state laser apparatus having the feature(xix), it is preferable that the high-index layers in thenegative-dispersion mirror be formed of one of a sulfide of Zn andoxides of Ti, Zr, Hf, Nb, Al, Zn, Y, Sc, La, Ce, Pr, and Ta, or acompound or mixture containing one or a combination of a sulfide of Znand oxides of Ti, Zr, Hf, Nb, Al, Zn, Y, Sc, La, Ce, Pr, and Ta.Specifically, it is preferable that the above compound or mixturecontain as one or more main components the one or combination of asulfide of Zn and oxides of Ti, Zr, Hf, Nb, Al, Zn, Y, Sc, La, Ce, Pr,and Ta, where the total fraction of the one or more main components is50 weight percent or more.

(xxii) In the mode-locked solid-state laser apparatus having the feature(xix), it is preferable that the low-index layers in thenegative-dispersion mirror be formed of one of an oxide of Si andfluorides of Ca, Li, Mg, Na, Th, Al, Hf, La, Y, and Zr, or a compound ormixture containing one or a combination of an oxide of Si and fluoridesof Ca, Li, Mg, Na, Th, Al, Hf, La, Y, and Zr. Specifically, it ispreferable that the above compound or mixture contain as one or moremain components the one or a combination of an oxide of Si and fluoridesof Ca, Li, Mg, Na, Th, Al, Hf, La, Y, and Zr, where the total fractionof the one or more main components is 50 weight percent or more.

The mode-locked solid-state laser apparatus according to the presentinvention has the following advantages.

In the mode-locked solid-state laser apparatus according to the presentinvention, the solid-state laser medium is arranged at a distance equalto or smaller than twice the Rayleigh range from the saturable absorbingmirror (i.e., the solid-state laser medium is arranged in close vicinityto or in contact with the saturable absorbing mirror). Therefore, thebeam waist of the oscillating light is not formed in the solid-statelaser medium, so that it is possible to have in the solid-state lasermedium a beam cross section necessary for achieving a sufficient gain.

On the other hand, in the mode-locked solid-state laser apparatus inwhich the SESAM is arranged in close vicinity to or in contact with thelaser medium, pulses competing with the soliton pulses preferentiallyacquire the gain because of the spatial hole burning. (That is, the gainadvantage of the pulses competing with the soliton pulses over thesoliton pulses increases.) Therefore, there is a fear that the solitonpulses cannot be stably generated. The present inventors have found thatstable soliton-mode oscillation can be realized by setting the depth ofabsorbing modulation at the saturable absorbing mirror to a value equalto or greater than 0.4%, and setting the total intracavity dispersion Dto a value realizing such a pulse bandwidth that the saturable absorbingmirror can suppress the pulses competing with the desired solitonpulses. Further, the present inventors have found that the necessarytotal intracavity dispersion D is negative and the necessary amount |D|of the negative total intracavity dispersion D can become thousands ofsquare femtoseconds in some cases. The conditions imposed on the totalintracavity dispersion D and the depth ΔR of absorbing modulation at thesaturable absorbing mirror for stably operating the small-sized,mode-locked solid-state laser apparatus have not been conventionallyknown. Therefore, conventionally, it has been difficult to realize asmall-sized, mode-locked solid-state laser apparatus which can stablyoperate. However, according to the present invention, it is possible torealize a mode-locked solid-state laser apparatus which can stablyoperate in a soliton mode.

Although, as JP11-168252A teaches, it is conventionally known that thesize of the laser apparatus can be reduced by using anegative-dispersion mirror as an output mirror, no concrete realizationof the negative-dispersion mirror which can also be used as an outputmirror is conventionally known. However, in order to optimumly outputlaser light, the present inventors have realized a negative-dispersionmirror which exhibits the transmittance of 0.5% to 3% (i.e., thereflectance of 99.5% to 97%), and imparts the (mirror) dispersion of−3000 fsec² to −600 fsec² to the light, where the transmittance of 0.5%to 3% has been determined to be the optimum transmittance by calculationon the basis of the laser gain and the loss in the resonator, and the(mirror) dispersion of −3000 fsec² to −600 fsec² has been determined soas to satisfy the condition imposed on the total intracavity dispersionD for realizing mode locking stability.

The magnitude of the above (mirror) dispersion of −3000 fsec² to −600fsec² according to the present invention is extremely great, comparedwith the conventional negative-dispersion mirror. Therefore, thenegative-dispersion mirror according to the present invention can makesufficient negative dispersion compensation by itself, so that it isunnecessary to further arrange a negative dispersion element in theresonator. That is, since, according to the present invention, thenegative-dispersion mirror can be used as the output mirror at one endof the resonator, the number of components of the mode-lockedsolid-state laser apparatus can be greatly reduced, so that themode-locked solid-state laser apparatus can be reduced in size, and beconstructed at low cost, and stably output laser light.

As explained above, according to the present invention, a condition forstably generating soliton pulses is clearly indicated, and thenegative-dispersion mirror realizing the dispersion and the reflectancesatisfying the condition is realized. Thus, cost reduction inmanufacture of the mode-locked solid-state laser apparatus anddownsizing of the mode-locked solid-state laser apparatus can beachieved. That is, it is possible to realize a highly-stable mode-lockedsolid-state laser apparatus having the synergetic advantages of low costand small size.

Further, in the case where a dichroic mirror which transmits the lightis arranged on the optical axis or on an extension of the optical axisso that when excitation light for exciting the solid-state laser mediumis injected into the resonator along a direction nonparallel to theoptical axis, the excitation light is reflected by the dichroic mirrorand propagates along the optical axis, the optical system for theexcitation light can be reduced in size. Therefore, the abovearrangement with the dichroic mirror is particularly preferable.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic side view illustrating an exemplary configurationof a mode-locked solid-state laser apparatus according to an embodimentof the present invention.

FIG. 2 illustrates examples of spectra (in the frequency domain),shapes, and timings of the desired soliton pulses and competing pulsesand a background.

FIG. 3 is a graph indicating examples of relationships between the pulsebandwidth and the gain advantages of pulses and a background competingwith mode-locked soliton pulses in a mode-locked solid-state laserapparatus in which the solid-state laser medium is Yb:KYW and the gain Gof the soliton pulses is 0.04.

FIG. 4 is a graph indicating examples of relationships between the pulsebandwidth and the necessary magnitude of dispersion in a mode-lockedsolid-state laser apparatus.

FIG. 5 is a graph indicating examples of relationships between the pulsebandwidth and the gain advantages of pulses and a background competingwith mode-locked soliton pulses in a mode-locked solid-state laserapparatus in which the solid-state laser medium is Yb:KYW and the gain Gof the mode-locked soliton pulses is 0.10.

FIG. 6 is a schematic cross-sectional view of a negative-dispersionmirror which can also be used as an output mirror.

FIG. 7 is a graph indicating examples of relationships between the pulsebandwidth and the gain advantages of pulses and a background competingwith mode-locked soliton pulses in a mode-locked solid-state laserapparatus in which the solid-state laser medium is Yb:YAG and the gain Gof the mode-locked soliton pulses is 0.07.

FIG. 8 is a graph indicating examples of relationships between the pulsebandwidth and the gain advantages of pulses and a background competingwith mode-locked soliton pulses in a mode-locked solid-state laserapparatus in which the solid-state laser medium is Yb:Y₂O₃ and the gainG of the mode-locked soliton pulses is 0.06.

FIG. 9 is a graph indicating examples of relationships between the pulsebandwidth and the gain advantages of pulses and a background competingwith mode-locked soliton pulses in a mode-locked solid-state laserapparatus in which the solid-state laser medium is Yb: Lu₂O₃ and thegain G of the mode-locked soliton pulses is 0.05.

FIG. 10 is a graph indicating examples of relationships between thepulse bandwidth and the gain advantages of pulses and a backgroundcompeting with mode-locked soliton pulses in a mode-locked solid-statelaser apparatus in which the solid-state laser medium is Er,Yb:glass andthe gain G of the mode-locked soliton pulses is 0.02.

FIG. 11 is a schematic side view illustrating an exemplary configurationof a mode-locked solid-state laser apparatus according to an embodimentof the present invention.

FIG. 12 is a graph indicating examples of relationships between thepulse bandwidth and the gain advantages of pulses and a backgroundcompeting with mode-locked soliton pulses in a mode-locked solid-statelaser apparatus in which the solid-state laser medium is Nd:glass andthe gain G of the mode-locked soliton pulses is 0.03.

FIG. 13A is a diagram indicating the optical thicknesses of the filmsconstituting a concrete example 1 of a negative-dispersion mirror.

FIG. 13B is a diagram indicating the reflectance and the dispersion inthe concrete example 1 of the negative-dispersion mirror.

FIG. 14A is a diagram indicating the optical thicknesses of the filmsconstituting a concrete example 2 of a negative-dispersion mirror.

FIG. 14B is a diagram indicating the reflectance and the dispersion inthe concrete example 2 of the negative-dispersion mirror.

FIG. 15A is a diagram indicating the optical thicknesses of the filmsconstituting a concrete example 3 of a negative-dispersion mirror.

FIG. 15B is a diagram indicating the reflectance and the dispersion inthe concrete example 3 of the negative-dispersion mirror.

FIG. 16A is a diagram indicating the optical thicknesses of the filmsconstituting a concrete example 4 of a negative-dispersion mirror.

FIG. 16B is a diagram indicating the reflectance and the dispersion inthe concrete example 4 of the negative-dispersion mirror.

FIG. 17 is a schematic side view illustrating an exemplary configurationof a mode-locked solid-state laser apparatus according to an embodimentof the present invention.

FIG. 18 is a schematic cross-sectional view of a negative-dispersionmirror used in the mode-locked solid-state laser apparatus of FIG. 17.

FIG. 19 is a schematic plan view illustrating a conventional mode-lockedsolid-state laser apparatus.

FIG. 20 is a schematic plan view illustrating a conventional mode-lockedsolid-state laser apparatus.

FIG. 21 is a schematic plan view illustrating a conventional mode-lockedsolid-state laser apparatus.

DESCRIPTION OF PREFERRED EMBODIMENTS

Embodiments of the present invention are explained in detail below withreference to drawings.

1. Apparatus Configuration (FIG. 1)

FIG. 1 is a schematic side view illustrating an exemplary configurationof a soliton mode-locked solid-state laser apparatus according to anembodiment of the present invention. The mode-locked solid-state laserapparatus of FIG. 1 comprises a semiconductor laser 11, an excitationoptical system 12, a dichroic mirror 13, a negative-dispersion mirror 5,a semiconductor saturable absorbing mirror (SESAM) 16, and a solid-statelaser medium 15. The semiconductor laser 11 emits excitation light(pumping light) 10. The excitation optical system 12 externally injectsthe excitation light 10 into a resonator in the mode-locked solid-statelaser apparatus of FIG. 1 along a direction nonparallel to the opticalaxis of the resonator. The dichroic mirror 13 is arranged in theresonator, and reflects the excitation light 10 toward the solid-statelaser medium 15, and transmits oscillating light 18, which resonates inthe resonator. The negative-dispersion mirror 5 realizes an end of theresonator, and has the function of an output mirror. The SESAM 16realizes the other end of the resonator. That is, the resonator isconstituted by the negative-dispersion mirror 5 and the SESAM 16. Thesolid-state laser medium 15 is arranged inside the resonator.

The solid-state laser medium 15 in the mode-locked solid-state laserapparatus of FIG. 1 is, for example, a Yb:KYW crystal. In this case, theexcitation light 10 emitted from the semiconductor laser 11 has thewavelength of 980 nm, which can excite the solid-state laser medium 15.The dichroic mirror 13 reflects the excitation light 10, and transmitsthe oscillating light 18, which has the wavelength of 1045 nm.

The solid-state laser medium 15 is arranged in close vicinity to (or incontact with) the SESAM 16 at a distance d equal to or smaller thantwice the Rayleigh range from the SESAM 16. The Rayleigh range isdefined on the basis of the mode radius in the resonator (i.e., the beamradius of the oscillating light).

In the above mode-locked solid-state laser apparatus, the excitationlight 10 is emitted from the semiconductor laser 11, and injectedthrough the excitation optical system 12 into the resonator along thedirection nonparallel to the optical axis of the resonator. Then, theexcitation light 10 is reflected by the dichroic mirror 13 and injectedinto the solid-state laser medium 15, so that the solid-state lasermedium 15 is excited, and light having the wavelength of 1045 nmgenerated by the excitation of the solid-state laser medium 15oscillates in the resonator. Part of the oscillating light passesthrough the negative-dispersion mirror 5 (which also behaves as theoutput mirror), and is externally outputted as output light 18 a. In themode-locked solid-state laser apparatus of FIG. 1, the beam waist of theoscillating light 18 is formed only on the SESAM 16.

In the mode-locked solid-state laser apparatus according to the presentinvention, the output light 18 a becomes pulsed light having a pulsewidth on the order of femtoseconds by a combined action of the negativegroup-velocity dispersion imparted by the negative-dispersion mirror 5and the self-phase compensation in the solid-state laser medium 15.Specifically, the SESAM 16 starts mode locking and maintains andstabilizes pulses, and soliton pulses are generated by a balance betweenthe group-velocity dispersion and the self-phase modulation. Thus, themode-locked pulses are steepened, so that stable generation of solitonpulses having a pulse width on the order of femtoseconds is enabled.

2. Arrangement of Laser Medium and SESAM

As described before, the distance between the solid-state laser mediumand the saturable absorbing mirror is at most twice the Rayleigh rangeaccording to the present invention. The present inventors have obtainedthe above condition on the distance in consideration of theaforementioned relationships (1) and (2) for realizing solitonmode-locked continuous pulse generation. When the beam radius of theoscillating light in the solid-state laser medium is too large, theoscillation threshold and the CW mode-locking threshold value become toohigh. In such a case, laser oscillation does not occur, or mode lockingdoes not occur, so that pulse oscillation becomes impossible. However,it is possible to achieve soliton mode locking in the case where thesolid-state laser medium is arranged at a distance equal to or smallerthan twice the Rayleigh range from the beam waist of the oscillatinglight.

In the case where the solid-state laser medium 15 is arranged at adistance approximately equal to twice the Rayleigh range from the SESAM16, the beam radius ω_(L) of the oscillating light in the solid-statelaser medium 15 becomes as large as 2.2 times the beam radius at thebeam waist. Therefore, on the basis of the relationship (1), the laseroscillation threshold in this case is estimated at 4.8 times the laseroscillation threshold in the case where the beam waist exists in thesolid-state laser medium 15. However, when the beam radius ω at the beamwaist is approximately 25 micrometers, the beam radius ω_(L) of theoscillating light in the solid-state laser medium 15 is 2.2×25micrometers, so that the laser oscillation threshold can be 100 mW orsmaller. In this case, the Rayleigh range is 1.9 mm, and twice theRayleigh range is 3.8 mm. Even in the case where the laser oscillationthreshold is 100 mW, oscillation with sufficiently high efficiency ispossible.

On the other hand, on the basis of the relationship (2), the CWmode-locking threshold in the case where the solid-state laser medium 15is arranged at a distance approximately equal to twice the Rayleighrange from the SESAM 16 is estimated at 5.93 nJ, while the CWmode-locking threshold in the case where the beam waist exists in thesolid-state laser medium 15 is estimated at 2.36 nJ. That is, the CWmode-locking threshold in the former case is approximately 2.5 times theCW mode-locking threshold in the latter case. (In the above estimationof the values of the CW mode-locking threshold, it is assumed that thedepth ΔR of the absorbing modulation in the SESAM 16 is 0.9%, and thesaturation fluence F_(sat,A) in the SESAM 16 is 90 μJ/cm².) However,even when the CW mode-locking threshold is increased as above, it ispossible to secure sufficient power of the oscillation output andachieve CW mode locking without a problem as long as the laseroscillation threshold is suppressed to 100 mW or below.

As explained above, when the solid-state laser medium 15 is arranged ata distance equal to or smaller than twice the Rayleigh range from theSESAM 16, it is possible to satisfy the relationships (1) and (2) andachieve downsizing of the mode-locked solid-state laser apparatus. Inother words, a small-sized solid-state laser apparatus which cangenerate mode-locked soliton pulses can be configured by arranging thesolid-state laser medium 15 at a distance equal to or smaller than twicethe Rayleigh range from the SESAM 16.

3. Suppression of Competing Pulses and Background

Nevertheless, as mentioned before, in the case where the solid-statelaser medium is arranged in close vicinity to an reflection mirror suchas the SESAM, spatial hole burning occurs, so that processes whichcompete with the process for generation of the mode-locked solitonpulses can occur. Therefore, even when the mode-locked soliton pulsesare generated, the mode-locked soliton pulses are disturbed by thepulses competing with the mode-locked soliton pulses.

The present inventors have found that when the mode-locked solid-statelaser apparatus is configured so that the depth ΔR of the absorbingmodulation and the total intracavity dispersion D are respectivelywithin predetermined ranges, the competing pulses generated by spatialhole burning can be suppressed, and stable generation of soliton pulsescan be achieved.

The present inventors have investigated the dependence of the gainadvantages ΔG, on the spectral bandwidth (wavelength bandwidth) Δλ_(P),of pulses and a background competing with mode-locked soliton pulses ina mode-locked solid-state laser apparatus having the configurationillustrated in FIG. 1. As mentioned before, the pulses and thebackground competing with mode-locked soliton pulses are considered tobe generated by spatial hole burning. The gain advantages ΔG have beenobtained by numerical calculation using the formulas indicated in thePaschotta reference.

FIG. 3 is a graph indicating examples of the dependences of the gainadvantages ΔG, on the spectral bandwidth (wavelength bandwidth) Δλ_(P),of pulses and a background competing with mode-locked soliton pulses ina mode-locked solid-state laser apparatus having the configurationillustrated in FIG. 1. In the numerical calculation for obtaining thedependences of FIG. 3, the solid-state laser medium is assumed to be aYb:KYW crystal, and the gain G of the mode-locked soliton pulses isassumed to be 0.04. (Although the gain G of the mode-locked solitonpulses depends on the power and the spot diameter of the excitationlight and details of the configuration of the mode-locked solid-statelaser apparatus, the value “0.04” of the gain G of the mode-lockedsoliton pulses is chosen as a typical value of the gain in a mode-lockedsolid-state laser apparatus having a practical configuration.)

The gain advantage ΔG is the difference of the gain of pulses generatedby each process competing with the process of generating the mode-lockedsoliton pulses from the gain of the mode-locked soliton pulses. FIG. 3shows that the gain of the pulses and the background generated by eachprocess competing with the process of generating the mode-locked solitonpulses is slightly greater than the gain of the mode-locked solitonpulses at any value of the pulse bandwidth. Therefore, in order torealize CW mode locking with the desired fundamental soliton pulses, itis necessary to suppress the above pulses and the background competingwith the desired fundamental soliton pulses.

The SESAM 16 exhibits a nonlinear reflection characteristic according tothe pulse energy E_(P). (For example, see the Hönninger reference.) Thenonlinear reflection characteristic of the SESAM 16 is effective insuppressing the CW background and the double pulses. Specifically, theCW background can be suppressed when the gain advantage ΔG(CW) of the CWbackground is equal to or smaller than half of the depth ΔR of theabsorbing modulation (i.e., ΔG(CW)≦ΔR/2), and the double pulses can besuppressed when the gain advantage ΔG(DP) of the double pulses is equalto or smaller than the value ΔR/S (i.e., ΔG(DP)≦ΔR/S), where S is thesaturation parameter at the SESAM, which is defined asS=E_(P)/(F_(sat,A)·A_(eff,A)). Thus, both of the CW background and thedouble pulses can be suppressed when the pulse bandwidth is such thatΔG(CW)≦ΔR/2 and ΔG(DP)≦ΔR/S.

On the other hand, the SESAM 16 cannot suppress the frequency-shiftedpulses. As mentioned before, the frequency-shifted pulses are equivalentto the mode-locked soliton pulses (repeated with the fundamentalrepetition period) in the pulse width, the pulse bandwidth, and thepulse energy, and are different from the mode-locked soliton pulses onlyin that the frequency is shifted from the mode-locked soliton pulses (asindicated in table 1 and FIG. 2). Therefore, the SESAM 16 exhibits anidentical saturation parameter S for either of the frequency-shiftedpulses and the mode-locked soliton pulses, so that the SESAM 16 cannotdiscriminate between the frequency-shifted pulses and the mode-lockedsoliton pulses.

Consequently, the mode-locked soliton pulses are stably generated whenthe pulse bandwidth is such that the gain advantage ΔG(SP) of thefrequency-shifted pulses is approximately zero, and ΔG(CW)≦ΔR/2 andΔG(DP)≦ΔR/S. Since the frequency-shifted pulses cannot be suppressed bythe SESAM, in many cases, the lower limit of the range of the values ofthe pulse bandwidth which realizes stable generation of the mode-lockedsoliton pulses is restricted by the frequency-shifted pulses.

In addition, the pulse width τ_(p) is proportional to the absolute value|D| of the total intracavity dispersion D as expressed by the equation(4).

$\begin{matrix}{\tau_{P} = {\frac{1.76{D}\lambda_{0}A_{{eff},L}}{4\; \pi \; n_{2}l_{S}}\frac{1}{E_{P}}}} & (4)\end{matrix}$

(See the Hönninger reference.) Further, the pulse width τ_(p) isinversely proportional to the pulse bandwidth.

In consideration of the above relationships, the present inventors havefound that since the range of the values of the pulse bandwidth whichallow stable generation of the mode-locked soliton pulses is restricted,the total intracavity dispersion D is also restricted. Then, the presentinventors have further found it necessary to set the total intracavitydispersion D to a value within an appropriate range according to thedepth ΔR of the absorbing modulation, for suppressing the spatial holeburning and stably generating mode-locked soliton pulses.

FIG. 4 is a graph indicating examples of the dependences of (theabsolute values |D| of) the total intracavity dispersions D on the pulsebandwidth, which are obtained on the basis of the equation (4). (Thepulse width τ_(p) is inversely proportional to the pulse bandwidth.)

In consideration of the above dependences of the gain advantages ΔG andthe total intracavity dispersion D on the pulse bandwidth, the presentinventors have found that when the depth ΔR of the absorbing modulationand the saturation parameter S at the saturable absorbing mirror satisfythe relationships,

ΔG(CW)≦ΔR/2 and ΔG(DP)≦ΔR/S, and   (A)

the mode-locked solid-state laser apparatus is configured so as to makethe total intracavity dispersion D (i.e., the dispersion D caused inlight having a predetermined wavelength during a round trip of the lightin the resonator) smaller than zero and make the absolute value |D| ofthe total intracavity dispersion D fall within a range in which therelationship expressed by the inequalities (A) are satisfied and thegain advantage ΔG(SP) is approximately zero, mode-locked soliton pulsescan be stably generated, where ΔG(CW) is the gain advantage of the CWbackground over the mode-locked soliton pulses, ΔG(DP) is the gainadvantage of the double pulses over the mode-locked soliton pulses, andΔG(SP) is the gain advantage of the frequency-shifted pulses over themode-locked soliton pulses.

Hereinbelow, the performance of the mode-locked solid-state laserapparatus according to the present invention is discussed below forcases where the above-mentioned parameters have various values.

Conventionally, the mode-locked solid-state laser apparatuses have beendesigned so that the saturation parameter S at the SESAM is in the rangefrom approximately three to five. Therefore, concrete examples of themode-locked solid-state laser apparatus according to the presentinvention explained below are assumed to be used in the same range ofthe saturation parameter S. Specifically, in the following explanations,the saturation parameter S at the SESAM is assumed to be four.

Referring to FIG. 3, the minimum gain advantage ΔG(DP) of the doublepulses is 0.05%. Therefore, ΔG·S=0.2%. In order to suppress the doublepulses when the saturation parameter S at the SESAM is 4, the depth ΔRof the absorbing modulation is required to be equal to or greater thanΔG·S=0.2%, i.e., ΔRmin≧ΔG·S=0.2%.

The depths ΔR of the absorbing modulation at the commercially availableSESAMs are at least approximately 0.3%. In the system in which spatialhole burning does not occur, the depth ΔR of approximately 0.3% to 2% isnormally considered to be appropriate for mode locking.

When ΔR=0.3% and S=4, in order to suppress the CW background, the pulsebandwidth is limited by the condition ΔG(CW)≦ΔR/2=0.15%. Therefore, FIG.3 shows that the CW background can be suppressed only when the pulsebandwidth is 4 to 7 nm. In addition, in order to suppress the doublepulses, the pulse bandwidth is also limited by the conditionΔG(DP)≦ΔR/S=0.075%. Therefore, FIG. 3 shows that the double pulses canbe suppressed only when the pulse bandwidth is 4.5 to 6.0 nm. Further,FIG. 3 shows that the frequency-shifted pulses can be suppressed onlywhen the pulse bandwidth is 4 nm or greater. Consequently, all of the CWbackground, the double pulses, and the frequency-shifted pulses can besuppressed only when the pulse bandwidth is 4.5 to 6.0 nm, which issubstantially determined by the condition for suppressing the doublepulses. Thus, (at the wavelength λ₀ of 1045 nm,) the minimum allowablepulse width (i.e., the duration of the Fourier transform limited pulse)is 254 to 191 femtoseconds (i.e., 223 fsec±14%). That is, the allowablerange of the values of the pulse width is extremely limited.

However, in order to secure an allowable range of the values of thepulse bandwidth with some margin, at least twice the minimum depth ΔRmin(=0.2%) of the absorbing modulation mentioned before is necessary. Thatis, the depth ΔR of the absorbing modulation at the SESAM required forwidening the allowable range of values of the pulse bandwidth is 0.4% orgreater. The depths ΔR of absorbing modulation in the practicable SESAMsare 0.4% or greater.

For example, when ΔR=0.8% and S=4, the pulse bandwidth ΔλP can be 4 to 8nm corresponding to the pulse width τ_(P)=287 to 143 fsec. Further, whenΔR=1.4% and S=4, the pulse bandwidth Δλ_(P) can be increased to 4 to 11nm corresponding to the pulse width τ_(P)=287 to 104 fsec.

Nevertheless, as explained above, even in the case where the depth ΔR ofthe absorbing modulation at the SESAM is 0.4% or greater, the range ofvalues of the pulse bandwidth in which the double pulses and the CWbackground can be suppressed is limited, so that the range of values ofthe pulse width is also limited.

Incidentally, in the case where a mode-locked solid-state laserapparatus has a 3-watt class semiconductor laser having the emitterwidth of 100 micrometers as the excitation light source, the resonatorlength of 50 mm, the transmission efficiency of 85%, the absorptionefficiency of 90%, the optical conversion efficiency of 30%, and theoutput mirror's transmittance T_(OC) of 1%, the internal energy E_(P) isapproximately 23 nJ. This is the maximum pulse energy which the concreteexamples of the mode-locked solid-state laser apparatus according to thepresent invention are supposed to have. (Theoretically, the small-sizedmode-locked solid-state laser apparatuses to which the present inventionis applied and which has a configuration as illustrated in FIG. 1 cannothave pulse energy exceeding the above value.)

According to the equation (4), the total intracavity dispersions D of−950 fsec² is necessary for generation of the pulses having a pulsewidth of 104 fsec (corresponding to the pulse bandwidth of 11 nm), andthe total intracavity dispersions D of approximately −2500 fsec² isnecessary for generation of the pulses corresponding to the pulsebandwidth of 4 nm. The pulse bandwidth of 4 nm is the lower limit of therange of values of the pulse bandwidth which allow stable generation ofmode-locked soliton pulses, and is determined by the frequency-shiftedpulses. In addition, the required total intracavity dispersion D is alsoa function of the pulse energy E_(P), and the magnitude of the requiredtotal intracavity dispersion D increases with increase in the pulseenergy E_(P). Therefore, the above value of approximately −2500 fsec² isthe upper limit of the absolute value of the required total intracavitydispersion D which is supposed to be realized in the mode-lockedsolid-state laser apparatus according to the present invention. Themagnitude of the required total intracavity dispersion D decreases withdecrease in the pulse energy E_(P), and the lower limit of the absolutevalue of the required total intracavity dispersion D is zero accordingto the equation (4).

For example, in the case where the mode-locked solid-state laserapparatus illustrated in FIG. 1 uses Yb:KYW as the solid-state lasermedium, and the depth ΔR of the absorbing modulation is equal to orgreater than 0.4%, the total intracavity dispersion D is generallyrequired to be in the range of −2500 fsec² to 0 fsec². However, inpractice, the range of the total intracavity dispersion D is furtherlimited according to the configuration of the mode-locked solid-statelaser apparatus. For example, the total intracavity dispersion D isrequired to be in the range of −2500 fsec² to −1400 fsec² when ΔR=0.8%,S=4, and E_(P)=20 nJ in the above mode-locked solid-state laserapparatus having the Yb:KYW laser medium, and the total intracavitydispersion D is required to be in the range of −2500 fsec² to −1000fsec² when ΔR=1.4%, S=4, and E_(P)=20 nJ in the above mode-lockedsolid-state laser apparatus having the Yb:KYW laser medium.

Further, when the mode-locked solid-state laser apparatus according tothe present invention is actually assembled, it is necessary to takeinto account the fact that the operation of the mode-locked solid-statelaser apparatus is likely to become unstable near an extremity of therange in which mode-locked soliton pulses can be stably generated.Therefore, it is preferable to configure the mode-locked solid-statelaser apparatus to realize the total intracavity dispersion D with amargin of approximately 20%. For example, when the above mode-lockedsolid-state laser apparatus having the Yb:KYW laser medium with ΔR=0.8%,S=4, and E_(P)=20 nJ is configured to realize the total intracavitydispersion D in the range of −2000 fsec² to −1700 fsec², the stabilityof the CW mode-locked operation of the mode-locked solid-state laserapparatus can be increased.

FIG. 5 is a graph indicating examples of the dependences of the gainadvantages ΔG, on the spectral bandwidth (wavelength bandwidth) Δλ_(P),of pulses and a background competing with mode-locked soliton pulses ina mode-locked solid-state laser apparatus having the configurationillustrated in FIG. 1. The gain advantages ΔG of FIG. 5 have also beenobtained by numerical calculation in a similar manner to FIG. 3. In thenumerical calculation for obtaining the dependences of FIG. 5, thesolid-state laser medium is assumed to be a Yb:KYW crystal, and the gainG of the mode-locked soliton pulses is assumed to be 0.1. As mentionedbefore, the pulses and the background competing with mode-locked solitonpulses are considered to be generated by spatial hole burning.

The comparison between the graphs of FIGS. 3 and 5 shows that theincrease in the gain (or increase in the excitation power) increases thegain advantages ΔG of the pulses and the CW background competing withmode-locked soliton pulses, and shifts the pulse bandwidths at which thegain advantages ΔG of the CW background and the double pulses areminimized, toward the direction of decreasing the pulse bandwidth. Inaddition, the comparison between the graphs of FIGS. 3 and 5 also showsthat the increase in the gain from G=0.04 to G=0.1 greatly reduces therange of values of the pulse bandwidth in which the pulses and the CWbackground competing with mode-locked soliton pulses are suppressed, andmakes the mode locking with a small pulse width difficult.

4. Negative-Dispersion Mirror

Next, the negative-dispersion mirror 5 used in the mode-lockedsolid-state laser apparatus of FIG. 1 is explained below.

FIG. 6 is a schematic cross-sectional view of an example of thenegative-dispersion mirror 5. The negative-dispersion mirror 5 isconstituted by a glass substrate 6, a dielectric multilayer structure 7,and an antireflection film 8. The glass substrate 6 has a concavesurface on one side, and the dielectric multilayer structure 7 is formedon the concave surface of the glass substrate 6. The antireflection film8 is formed on another surface of the glass substrate 6 opposite to theconcave surface.

The dielectric multilayer structure 7 is constituted by two multilayermirrors ML₁ and ML₂ and a cavity layer C. The cavity layer C issandwiched between the two multilayer mirrors ML₁ and ML₂ and causesresonance of light L having the predetermined wavelength between the twomultilayer mirrors ML₁ and ML₂. The example of the negative-dispersionmirror 5 illustrated in FIG. 6 has only one cavity layer C in thedielectric multilayer structure 7. The antireflection film 8 is arrangedfor preventing reflection of the light which passes through thedielectric multilayer structure 7, at the surface of the glass substrate6 opposite to the concave surface. Thus, 97% to 99.5% of the lightLwhich enters the negative-dispersion mirror 5 from the side of thedielectric multilayer structure 7 is reflected by the dielectricmultilayer structure 7 (i.e., the reflectance of the light L by thedielectric multilayer structure 7 is 97% to 99.5%), and 3% to 0.5% ofthe light L passes through the dielectric multilayer structure 7, theglass substrate 6, and the antireflection film 8.

The layers constituting the dielectric multilayer structure 7 are formedon the concave surface of the glass substrate 6 in the order asindicated in FIG. 6, where the first to (k−1)-th layers constitute themultilayer mirror ML₁, the k-th layer realizes the cavity layer C, andthe (k+1)-th to n-th layers constitute the multilayer mirror ML₂.

The negative-dispersion mirror 5 imparts a mirror dispersion of −3000fsec² to −600 fsec² to the light L (the oscillating light 18) having theaforementioned wavelength, and the reflectance of the light L by thedielectric multilayer structure 7 is 97% to 99.5%. Further, when thelight L has a bandwidth of 10 nm containing the above predeterminedwavelength, the negative-dispersion mirror 5 imparts to the light amirror dispersion of −3000 fsec² to −600 fsec², and the reflectance ofthe light by the dielectric multilayer structure 7 is 97% to 99.5%. Inthe negative-dispersion mirror 5, the values of the mirror dispersionand the reflectance can be arbitrarily set in the above ranges,respectively.

It is preferable that each of the two multilayer mirrors ML₁ and ML₂ inthe negative-dispersion mirror 5 be constituted by high-index layershaving a high refractive index nm₁ and low-index layers having a lowrefractive index nm₂ (<nm₁) which are alternately laminated, and thetotal number of the high-index layers and the low-index layers in eachof the two multilayer mirrors ML₁ and ML₂ be eight or greater. Forexample, the odd-numbered layers (including the first layer, the thirdlayer, . . . ) are high-index layers, and the even-numbered layers(including the second layer, the fourth layer, . . . ) are low-indexlayers. When each of the two multilayer mirrors ML₁ and ML₂ isconstituted by eight or more layers, the negative-dispersion mirror 5can sufficiently achieve the reflectance of 97% or higher.

The high-index layers in the negative-dispersion mirror 5 may be formedof one of a sulfide of Zn and oxides of Ti, Zr, Hf, Nb, Al, Zn, Y, Sc,La, Ce, Pr, and Ta, or a compound or mixture containing one or acombination of a sulfide of Zn and oxides of Ti, Zr, Hf, Nb, Al, Zn, Y,Sc, La, Ce, Pr, and Ta. Specifically, the high-index layers may beformed of TiO₂, Ta₂O₅, ZrO₂, Substance H4, or the like, where SubstanceH4 (a product of Merck KGaA, Germany) is an evaporation material mainlycontaining LaTi_(x)O_(y).

In addition, the low-index layers in the negative-dispersion mirror 5may be formed of one of an oxide of Si and fluorides of Ca, Li, Mg, Na,Th, Al, Hf, La, Y, and Zr, or a compound or mixture containing one or acombination of an oxide of Si and fluorides of Ca, Li, Mg, Na, Th, Al,Hf, La, Y, and Zr. Specifically, the low-index layers may be formed ofSiO₂, MgF, Al₂O₃, and the like.

However, the constituent materials of the high-index layers and thelow-index layers are not limited to the above materials. The high-indexlayers and the low-index layers may be formed of any other materials aslong as the refractive indexes of the high-index layers are higher thanthe refractive indexes of the lower-index layers.

The refractive index of the cavity layer C is not specifically limited.For example, the cavity layer C may be formed of one of the materials ofwhich the high-index layers and the low-index layers are formed. In thiscase, it is possible to prevent increase in the cost and the number ofprocess steps.

The optical thickness of the cavity layer C is generally greater thanthe other layers. In the present embodiment, the optical thickness ofthe cavity layer C is equal to or greater than twice the quarterwavelength λ/4 (i.e., half of the predetermined wavelength Δ of theaforementioned light L), and is preferably four to eight times thequarter wavelength Δ/4. The optical thickness of each of layersconstituting the two multilayer mirrors ML₁ and ML₂ in thenegative-dispersion mirror 5 is equal to or greater than half of thequarter wavelength Δ/4 and smaller than twice the quarter wavelength Δ/4(i.e., equal to or greater than one-eighth of the predeterminedwavelength Δ and smaller than half of the predetermined wavelength Δ).The optical thickness of a film is defined as the product of refractiveindex n of the film and the film thickness d.

5. Other Features of Apparatus

The light L having the predetermined wavelength is the oscillating light18, which is emitted from the solid-state laser medium 15 and isoscillating in the resonator. Therefore, the light L is determinedaccording to the configuration of the mode-locked solid-state laserapparatus in which the negative-dispersion mirror 5 is used. Forexample, the wavelength Δ of the light L is 1045 nm in the case wherethe solid-state laser medium is Yb:KYW (KY(WO₄)₂), 1040 nm in the casewhere the solid-state laser medium is Yb:KGW (KGd(WO₄)₂), 1050 nm in thecase where the solid-state laser medium is Yb:YAG, and 1076 nm in thecase where the solid-state laser medium is Yb:Y₂O₃.

As mentioned before, the excitation light 10 is injected into theresonator along a direction nonparallel to the optical axis of theresonator, and is then reflected by the dichroic mirror 13 so as to beinjected into the solid-state laser medium 15. The dichroic mirror 13 isarranged on the optical axis of the resonator, and highly reflects theexcitation light. (For example, the dichroic mirror 13 reflects theexcitation light with a reflectance higher than 85%). The dichroicmirror 13 substantially transmits the oscillating light. (For example,the dichroic mirror 13 reflects the oscillating light with a reflectancelower than 0.5%). Therefore, the lowering of the laser oscillationefficiency due to the insertion of the dichroic mirror 13 can beminimized, and the excitation light source can be arranged close to thesolid-state laser medium, compared with the case where the conventionaloptical system is used. It is preferable to arrange the excitationoptical system 12 and the dichroic mirror 13 so that the excitationlight is incident on the dichroic mirror 13 at an incident angle equalto 45 degrees or the Brewster's angle. In addition, the dichroic mirror13 should be coated according to the incident angle of the excitationlight.

Further, since the dichroic mirror 13 is arranged in the resonator asabove, the excitation optical system 12 can be realized by a single lenssuch as a graded-index lens (GRIN lens) in order to reduce the distancebetween the solid-state laser medium and the lens in the excitationoptical system 12. For example, in the case where a GRIN lens having apitch of 0.23, an effective focal length of 1.94 mm, a lens length of4.42 mm, and a lens diameter of 1.8 mm (available from Thorlabs JapanInc.) is used for realizing a focusing system of 1:2 magnification asthe excitation optical system 12, the distance from the excitation-lightsource to the solid-state laser medium is approximately 8.3 mm, which isthe sum of the distance, d1=2/3f=1.3 mm, from the excitation-lightsource to the front-side principal point of the lens, the lens length of4.4 mm, and the distance, d2=2×d1=2.6 mm, from the rear-side principalpoint of the lens to the solid-state laser medium. That is, the distancefrom the excitation-light source to the solid-state laser medium is verysmall. On the other hand, in the case where the conventional opticalsystem illustrated in FIG. 19 is used (i.e., the excitation light isinjected through the concave output mirror) for realizing a focusingsystem of 1:2 magnification, the distance from the excitation-lightsource to the solid-state laser medium is at least 75 to 200 mm. Thus,according to the present invention, the dimension of the excitationoptical system 12 can be remarkably reduced.

Although the stability of generation of the mode-locked soliton pulsesis explained before for the exemplary case where the resonator length is50 mm, it is possible to achieve the stability of both of the laserresonator and the mode locking as long as the length of the resonatordoes not exceed 200 mm, for the reason explained below.

When the length of the resonator is increased, the pulse repetition ratedecreases, and the pulse energy increases, so that the CW mode-lockingthreshold can be more easily exceeded. Therefore, on the basis of theequation (2) as the condition for preventing the Q-switching operationduring the soliton mode locking, it can be considered that greater pulseenergy and longer resonator length are more preferable.

However, from the viewpoint that the mechanical variations causeinstability of the laser output, there is a limit to the resonatorlength. The mechanical limit of the resonator length is obtained asapproximately 200 mm from the following consideration.

In many solid-state laser apparatuses having a resonator length ofapproximately 1 m, optical misalignment caused by mechanical vibrationsand drifts, thermal displacement of structural components, flexure, andthe like deteriorates the laser characteristics and makes the laseroperation unstable. The alignment tolerance of the resonator is known tobe reversely proportional to the resonator length and a function of themirror curvature. For example, the alignment tolerance of the one-meterclass resonator is known to be approximately 50 to 100 μrad. (Forexample, see N. Hodgson and H. Weber, “Optical Resonators: Fundamentals,Advanced Concepts and Applications”, Springer, pp. 214-223, 2007.)Therefore, when the resonator length is reduced to 200 mm or smaller,the alignment tolerance of the resonator can be five times increased to250 to 500 μrad. Although the mechanical vibrations of the mirrorscannot be unconditionally quantified, a catalog of Newport Corporationreports that the mechanical vibrations of a mirror when a common gimbalmount is used is 50 μrad under temperature variations of 8 degreescentigrade. In such a case, the mechanical vibrations of a mirror isequivalent to the alignment tolerance of the one-meter class resonator,and is approximately one-fifth of the alignment tolerance of resonatorshaving the length of 200 mm or smaller. That is, in the solid-statelaser apparatuses having the resonator length of 200 mm or smaller, themechanical vibrations of a mirror are considered to be ignorable.

Consequently, when the resonator length is 200 mm or smaller, it ispossible to achieve the stability of both of the laser resonator and themode locking. Therefore, it is preferable that the resonator length notexceed 200 mm.

6. Other Solid-State Laser Mediums

Although the stability of generation of the mode-locked soliton pulsesis explained before for the exemplary case where the solid-state lasermedium is Yb:KYW, calculation results similar to FIGS. 3 and 5 can alsobe obtained even in the case where the solid-state laser medium is aYb:KGW crystal since the physical properties such as the fluorescentbandwidth, the induced-emission cross section, and the absorption crosssection of the Yb:KYW and Yb:KGW are approximately identical except thatthe nonlinear refractive index n₂ (=20×10⁻²⁰ m²/W) of Yb:KGW isapproximately 2.3 times the nonlinear refractive index n₂ (=8.7×10⁻²⁰m²/W) of Yb:KYW. Therefore, the magnitude of the total intracavitydispersion D in the mode-locked solid-state laser apparatus in whichYb:KGW is used becomes approximately 2.3 times the magnitude of thetotal intracavity dispersion D in the mode-locked solid-state laserapparatus in which Yb:KYW is used. (The latter is indicated in FIG. 4.)That is, in the mode-locked solid-state laser apparatus in which Yb:KGWis used, it is preferable that the total intracavity dispersion D beequal to or greater than −5750 fsec² and smaller than 0 fsec².

FIG. 7 is a graph indicating examples of the dependences of the gainadvantages ΔG, on the spectral bandwidth (wavelength bandwidth) Δλ_(P),of pulses and a background competing with mode-locked soliton pulses ina mode-locked solid-state laser apparatus having the configurationillustrated in FIG. 1 in which the solid-state laser medium 15 is Yb:YAGand oscillation at the wavelength of 1050 nm occurs. The dependences ofFIG. 7 are also obtained by numerical calculation in a similar manner toFIG. 3. In the numerical calculation for obtaining the dependences ofFIG. 7, the gain G of the mode-locked soliton pulses is assumed to be0.07.

On the basis of the dependences of the gain advantages ΔG indicated inFIG. 7, it is understood that a bandwidth which realizes stablegeneration of mode-locked soliton pulses can be obtained when thesaturation parameter S is 4 and the depth ΔR of the absorbing modulationis equal to or greater than 0.4%. For example, in the case whereΔR=0.8%, the double pulses and the CW background can be suppressed whenthe bandwidth is 2 to 4 nm. In the case where the depth ΔR of theabsorbing modulation is further increased, the mode-locked solitonpulses can be stably generated with a greater bandwidth. In practice, itis preferable to realize mode locking which generates soliton pulseswith a short pulse width of approximately 300 fsec or smaller.Therefore, it is preferable that the pulse bandwidth be approximately 4nm (corresponding to the pulse width of 287 fsec) or greater. Thus, inthe case where the solid-state laser medium 15 is Yb:YAG, it ispreferable that ΔR≧0.8%. Since the nonlinear refractive index n₂(=6.2×10⁻²⁰ m²/W) of Yb:YAG is approximately 70% of the nonlinearrefractive index n₂ of Yb:KYW, the preferable range of the magnitude ofthe total intracavity dispersion D in the mode-locked solid-state laserapparatus in which Yb:YAG is used is approximately 70% of the preferablerange of the magnitude of the total intracavity dispersion D in themode-locked solid-state laser apparatus in which Yb:KYW is used. Thatis, the total intracavity dispersion D in the mode-locked solid-statelaser apparatus in which Yb:YAG is used is preferably equal to orgreater than −1750 fsec² and smaller than 0 fsec².

The solid-state laser mediums formed of ceramics are currently receivingattention, and can be used as the solid-state laser medium 15 in themode-locked solid-state laser apparatus according to the presentinvention. Although the solid-state laser mediums are normally acrystal, some solid-state laser mediums of garnet-group materials (suchas YAG) can be ceramic materials. While the ceramic materials exhibitoptical characteristics equivalent or superior to the crystallinematerials, the use of the ceramic materials enables formation oflarge-sized solid-state laser mediums and cost reduction. Besides thegarnet-group materials, the so-called C-rare earth materials (such asYb:Y₂O₃, Yb:Sc₂O₃, and Yb:Lu₂O₃) can also be formed into ceramics. (SeeA. Shirakawa et al., “Diode-pumped mode-locked Yb³⁺:Y₂O₃ ceramic laser”,Optics Express, Vol. 11, No. 22, pp. 2911-2916, 2003.) Further, someother materials (such as glass) which can inherently be formed into alarge-sized body at low cost have already been used as solid-state lasermediums. For example, laser devices using Yb-doped glass orEr,Yb-codoped glass and emitting wideband light have been reported. (SeeG. J. Spuhler et al., “Soliton mode-locked Er:Yb:glass laser”, OpticsLetters, Vol. 30, Issue 3, pp. 263-265, 2005.) The present invention canalso be applied to such laser devices.

FIG. 8 is a graph indicating examples of the dependences of the gainadvantages ΔG, on the spectral bandwidth (wavelength bandwidth) Δλ_(P),of pulses and a background competing with mode-locked soliton pulses ina mode-locked solid-state laser apparatus having the configurationillustrated in FIG. 1 in which the solid-state laser medium 15 isYb:Y₂O₃. The dependences of FIG. 8 are also obtained by numericalcalculation in a similar manner to FIG. 3. In the numerical calculationfor obtaining the dependences of FIG. 8, the gain G of the mode-lockedsoliton pulses is assumed to be 0.06.

On the basis of the dependences of the gain advantages ΔG indicated inFIG. 8, it is understood that a bandwidth which realizes stablegeneration of mode-locked soliton pulses can be obtained when thesaturation parameter S is 4 and the depth ΔR of the absorbing modulationis equal to or greater than 0.4%. For example, in the case whereΔR=0.8%, the double pulses and the CW background can be suppressed whenthe bandwidth is 4 to 6 nm. While the bandwidth which suppresses thedouble pulses and the CW background when ΔR=0.4% is limited to only thevicinity of 4 nm, the double pulses and the CW background can besuppressed in a wider range of bandwidths when ΔR=0.8%.

In addition, since the nonlinear refractive index n₂ (=1.16×10⁻¹⁹ m²/W)of Yb:Y₂O₃, is approximately 1.3 times the nonlinear refractive index n₂of Yb:KYW, the preferable range of the magnitude of the totalintracavity dispersion D in the mode-locked solid-state laser apparatusin which Yb:Y₂O₃ is used is approximately 1.3 times the preferable rangeof the magnitude of the total intracavity dispersion D in themode-locked solid-state laser apparatus in which Yb:KYW is used. Thatis, the total intracavity dispersion D in the mode-locked solid-statelaser apparatus in which Yb:Y₂O₃ is used is preferably equal to orgreater than −3250 fsec² and smaller than 0 fsec².

FIG. 9 is a graph indicating examples of the dependences of the gainadvantages ΔG, on the spectral bandwidth (wavelength bandwidth) Δλ_(P),of pulses and a background competing with mode-locked soliton pulses ina mode-locked solid-state laser apparatus having the configurationillustrated in FIG. 1 in which the solid-state laser medium 15 isYb:Lu₂O₃. The dependences of FIG. 9 are also obtained by numericalcalculation in a similar manner to FIG. 3. In the numerical calculationfor obtaining the dependences of FIG. 9, the gain G of the mode-lockedsoliton pulses is assumed to be 0.05.

On the basis of the dependences of the gain advantages ΔG indicated inFIG. 9, it is understood that a bandwidth which realizes stablegeneration of mode-locked soliton pulses can be obtained when thesaturation parameter S is 4 and the depth ΔR of the absorbing modulationis equal to or greater than 0.4%. When the depth ΔR of the absorbingmodulation is further increased, the mode-locked soliton pulses can bestably generated in a wider range of bandwidths.

In addition, since the nonlinear refractive index n₂ (=1.0×10⁻¹⁹ m²/W)of Yb:Lu₂O₃, is approximately 1.2 times the nonlinear refractive indexn₂ of Yb:KYW, the preferable range of the magnitude of the totalintracavity dispersion D in the mode-locked solid-state laser apparatusin which Yb: Lu₂O₃ is used is approximately 1.2 times the preferablerange of the magnitude of the total intracavity dispersion D in themode-locked solid-state laser apparatus in which Yb:KYW is used. Thatis, the total intracavity dispersion D in the mode-locked solid-statelaser apparatus in which Yb:Lu₂O₃ is used is preferably equal to orgreater than −3000 fsec² and smaller than 0 fsec².

Further, since Yb:Sc₂O₃ has an identical crystal structure and anapproximately equivalent nonlinear refractive index to Yb:Lu₂O₃.Therefore, the condition imposed, for realizing stable generation ofmode-locked soliton pulses, on the mode-locked solid-state laserapparatus using Yb:Sc₂O₃ is similar to the condition imposed on themode-locked solid-state laser apparatus using Yb:Lu₂O₃.

FIG. 10 is a graph indicating examples of the dependences of the gainadvantages ΔG, on the spectral bandwidth (wavelength bandwidth) Δλ_(P),of pulses and a background competing with mode-locked soliton pulses ina mode-locked solid-state laser apparatus having the configurationillustrated in FIG. 1 in which the solid-state laser medium 15 isEr,Yb-codoped phosphate glass. The dependences of FIG. 10 are alsoobtained by numerical calculation in a similar manner to FIG. 3. In thenumerical calculation for obtaining the dependences of FIG. 10, the gainG of the mode-locked soliton pulses is assumed to be 0.02.

In the Er,Yb-codoped phosphate glass, the excitation light is absorbedby the Yb ions, and the excitation energy is transferred from the Ybions to the Er ions. Since the phonon energy of the phosphate glass isrelatively great, Er ions at the excited level ⁴I_(11/2) last relax tothe upper laser level ⁴I_(13/2). Thus, inverted population can be formedwith high efficiency. In this case, the excitation light has thewavelength of approximately 980 nm, and the oscillating light has thewavelength of approximately 1550 nm.

In the case where the Er,Yb-codoped phosphate glass is used as thesolid-state laser medium 15 in the mode-locked solid-state laserapparatus of FIG. 1, it is possible to obtain the oscillating light 18having a wavelength of 1550 nm to 1600 nm. Alternatively, in the casewhere the mode-locked solid-state laser apparatus having theconfiguration as illustrated in FIG. 11 is used, it is possible toobtain the second harmonic wave 61 having a wavelength of 780 nm to 800nm. The configuration of FIG. 11 is different from the configuration ofFIG. 1 in that a nonlinear optical crystal 60 is arranged on the outsideof the configuration of FIG. 1, so that the oscillating light 18 aoutputted through the negative-dispersion mirror 5 enters the nonlinearoptical crystal 60, and the second harmonic wave 61 is generated. Theconventional solid-state laser apparatuses emitting light at thewavelength around 800 nm need, for example, a crystal doped with atransmission metal such as Ti:Sapphire and a green laser which emitslight at the wavelength of 532 nm. On the other hand, the mode-lockedsolid-state laser apparatus of FIG. 11 is advantageous in thatexcitation with a semiconductor laser in the infrared band andutilization of inherently-high-efficiency transition in a rare-earthelement are enabled.

In the Er,Yb-codoped phosphate glass, the frequency-shifted pulses canbe suppressed to approximately zero when the pulse bandwidth is 2 nm orgreater. In practice, it is preferable to realize mode locking withsoliton pulses having a short pulse width of 600 fsec or smaller.Therefore, it is preferable that the pulse bandwidth be approximately 4nm (corresponding to the pulse width of 600 fsec) or greater.

In addition, since the nonlinear refractive index n₂ (=3×10⁻²⁰ m²/W) ofEr,Yb-codoped phosphate glass is small, the total intracavity dispersionD in the mode-locked solid-state laser apparatus in which Er,Yb-codopedphosphate glass is used is preferably equal to or greater than −1200fsec² and smaller than 0 fsec².

The condition on the total intracavity dispersion D in the mode-lockedsolid-state laser apparatus in which Nd-doped laser glass is used as thesolid-state laser medium 15 can be obtained in a similar manner to thecondition in the case where Er,Yb-codoped phosphate glass is used. Forexample, FIG. 12 is a graph indicating examples of the dependences ofthe gain advantages ΔG, on the spectral bandwidth (wavelength bandwidth)Δλ_(P), of pulses and a background competing with mode-locked solitonpulses in a mode-locked solid-state laser apparatus having theconfiguration illustrated in FIG. 1 in which the solid-state lasermedium 15 is Nd-doped phosphate glass. The dependences of FIG. 12 arealso obtained by numerical calculation in a similar manner to FIG. 3. Inthe numerical calculation for obtaining the dependences of FIG. 12, thegain G of the mode-locked soliton pulses is assumed to be 0.03.

For the reason explained before, it is preferable that the depth ΔR ofthe absorbing modulation be equal to or greater than 0.4%. Since thenonlinear refractive index n₂ (=2.8×10⁻²⁰ m²/W) of Nd-doped phosphateglass is small, the total intracavity dispersion D in the mode-lockedsolid-state laser apparatus in which Nd-doped phosphate glass is used ispreferably equal to or greater than −800 fsec² and smaller than 0 fsec².

7. Examples of Negative-Dispersion Mirror

Hereinbelow, the layers constituting concrete examples 1 to 4 of thenegative-dispersion mirror are explained with reference to FIGS. 13A,13B, 14A, 14B, 15A, 15B, 16A, and 16B. Each of FIGS. 13A, 14A, 15A, and16A indicates the optical thicknesses of the films constituting one ofthe concrete examples 1 to 4 of the negative-dispersion mirror, wherethe optical thicknesses are determined on the basis of the centralwavelength. Each of FIGS. 13B, 14B, 15B, and 16B is a graph indicatingthe reflectance and the negative dispersion which are estimated, bysimulation, to be realized by the layered structure of one of theconcrete examples 1 to 4 of the negative-dispersion mirror. The concreteexamples 1 to 4 are designed on the assumption that the solid-statelaser medium 15 is Yb:KYW and the central wavelength is 1045 nm.

In each of FIGS. 13A, 14A, 15A, and 16A, the layer numbers are indicatedalong the abscissa, and the optical thickness n·d, normalized by λ/4, isindicated along the ordinate. The first layer is the nearest to thesubstrate, and the fiftieth layer is the farthest from the substrate. Ineach of FIGS. 13B, 14B, 15B, and 16B, the wavelength (nm) of the light Lis indicated along the abscissa, and the reflectance (%) and thenegative dispersion (fsec²) are indicated along the ordinate.

In the concrete example 1 having the layered structure indicated in FIG.13A, the first to eighth layers constitute the multilayer mirror ML₁,the ninth layer realizes the cavity layer C, and the tenth to fiftiethlayers constitute the multilayer mirror ML₂. That is, the cavity layer Cis arranged relatively near to the substrate. In addition, as indicatedin FIG. 13B, the negative-dispersion mirror having the layered structureindicated in FIG. 13A has the reflectance of 98.5% and imparts to thelight the negative mirror dispersion of −1000 fsec² at least in thewavelength band of 1040 to 1050 nm.

In the concrete example 2 having the layered structure indicated in FIG.14A, the first to thirty-fourth layers constitute the multilayer mirrorML₁, the thirty-fifth layer realizes the cavity layer C, and thethirty-sixth to fiftieth layers constitute the multilayer mirror ML₂.That is, the position of the cavity layer C in the concrete example 2 isfarther from the substrate than in the concrete example 1. In addition,as indicated in FIG. 14B, the negative-dispersion mirror having thelayered structure indicated in FIG. 14A has the reflectance of 98.5% andimparts to the light the negative mirror dispersion of −1000 fsec² atleast in the wavelength band of 1040 to 1050 nm.

As indicated above, although the concrete examples 1 and 2 are differentin the layered structure, the concrete examples 1 and 2 haveapproximately identical properties in the wavelength band of 1040 to1050 nm.

In the concrete example 3 having the layered structure indicated in FIG.15A, the first to thirtieth layers constitute the multilayer mirror ML₁,the thirty-first layer realizes the cavity layer C, and thethirty-second to fiftieth layers constitute the multilayer mirror ML₂.In addition, as indicated in FIG. 15B, the negative-dispersion mirrorhaving the layered structure indicated in FIG. 15A has the reflectanceof 98.5% and imparts to the light the negative mirror dispersion of−3000 fsec² at least in the wavelength band of 1040 to 1050 nm.

In the concrete example 4 having the layered structure indicated in FIG.16A, the first to thirtieth layers constitute the multilayer mirror ML₁,the thirty-first layer realizes the cavity layer C, and thethirty-second to fiftieth layers constitute the multilayer mirror ML₂.As indicated in FIG. 16B, the negative-dispersion mirror having thelayered structure indicated in FIG. 16A has the reflectance of 98.5% andimparts to the light the negative mirror dispersion of −600 fsec² atleast in the wavelength band of 1040 to 1050 nm.

The concrete examples 3 and 4 are identical in the ordinal position ofthe cavity layer C and the total number of constituent layers, andapproximately identical in the total optical thickness. However, theconcrete examples 3 and 4 are greatly different in the properties. Thisdifference is considered to be caused by the differences in the opticalthicknesses of the respective layers constituting thenegative-dispersion mirror.

In each of the concrete examples 1, 2, 3, and 4, the optical thickness,normalized by λ/4, of the cavity layer C is 4 to 5, the opticalthickness, normalized by λ/4, of each of the layers constituting themultilayer mirrors ML₁ and ML₂ is equal to or greater than 0.5 andsmaller than 2. However, the normalized optical thickness of the cavitylayer C is not limited to the range of 4 to 5, and may be any valueequal to or greater than 2. In addition, the total number of the layersconstituting the multilayer structure of the negative-dispersion mirroris not limited to fifty. Further, although the central wavelength is1045 nm in the case where the solid-state laser medium is Yb:KYW,generally, the central wavelength λ is determined according to thesolid-state laser medium arranged in the mode-locked solid-state laserapparatus.

Generally, the multilayer structure of the negative-dispersion mirrorcan be determined as follows.

(1) The central wavelength λ is determined according to the solid-statelaser medium arranged in the mode-locked solid-state laser apparatus.

(2) A desired value of the mirror dispersion in the range of −3000 fsec²to −600 fsec² and a desired value of the reflectance at thenegative-dispersion mirror in the range of 97% to 99.5% are set.

(3) Rough estimates of values specifying the multilayer structure andthe values of the thicknesses of the layers are set as initialconditions in computer simulation. At this time, the values specifyingthe multilayer structure include the values of the total number oflayers, the refractive indexes (the constituent materials) of thelayers, the position of the cavity layer C, the number of the layersconstituting the multilayer mirrors, and the optical thickness of eachof the layers constituting the multilayer mirrors. For example, theoptical thickness of each of the layers constituting the multilayermirrors may be set to a value near a quarter of the central wavelength(λ/4), and the optical thickness of the cavity layer C may be set to avalue near an integer multiple a quarter of the central wavelength(λ/4×n).

(4) The computer simulation is performed by using the thin-filmcalculation software “Essential Macleod,” and then the above initialconditions specifying the multilayer structure and the values of thethicknesses of the layers are manually or automatically corrected untilthe multilayer structure of the negative-dispersion mirror is finallyobtained.

8. Variation of Apparatus Configuration (FIG. 17)

Although it is preferable that the resonator have a linear shape,generally, the resonator may have any shape as long as the solid-statelaser medium 15 is arranged in close vicinity to or in contact with theSESAM 16. In addition, although the negative-dispersion mirror in themode-locked solid-state laser apparatus of FIG. 1 or 11 has a concavemirror, the negative-dispersion mirror may have a structure in which amultilayer is formed on a flat substrate.

FIG. 17 is a schematic side view illustrating an exemplary configurationof a mode-locked solid-state laser apparatus according to an embodimentof the present invention. The mode-locked solid-state laser apparatus ofFIG. 17 is different from the mode-locked solid-state laser apparatus ofFIG. 1 in that the mode-locked solid-state laser apparatus of FIG. 17has a V-shaped resonator, the negative-dispersion mirror 1 (instead ofthe negative-dispersion mirror 5) is arranged as an output mirror, and aconcave mirror 19 is arranged in the resonator so as to reflect theoscillating light 18. In the negative-dispersion mirror 1, a multilayerstructure 4 is formed on a flat substrate 3.

FIG. 18 is a schematic cross-sectional view of an example of thenegative-dispersion mirror 1 used in the mode-locked solid-state laserapparatus of FIG. 17. As illustrated in FIG. 18, the negative-dispersionmirror 1 is a mirror having a dielectric multilayer structure 4 on aflat glass substrate 3. The dielectric multilayer structure 4 isconstituted by two multilayer mirrors ML₁′ and ML₂′ and a cavity layerC′. The cavity layer C′ is sandwiched between the two multilayer mirrorsML₁′ and ML₂′ and causes resonance of light L having the predeterminedwavelength between the two multilayer mirrors ML₁′ and ML₂′. Thenegative-dispersion mirror 1 imparts a mirror dispersion of −3000 fsec²to −600 fsec² to the light L having the aforementioned wavelength, andthe reflectance of the light L by the dielectric multilayer structure 4is 97% to 99.5%. For example, in the case where the solid-state lasermedium 15 is Yb:KYW, and the predetermined wavelength is 1045 nm, thetwo multilayer mirrors ML₁′ and ML₂′ and the cavity layer C′ in thenegative-dispersion mirror 1 may be arranged in the order similar to theorder in which the multilayer mirrors ML₁ and ML₂ and the cavity layer Cin one of the aforementioned concrete examples 1 to 4 are arranged, andmay have optical thicknesses respectively similar to the multilayermirrors ML₁ and ML₂ and the cavity layer C in one of the aforementionedconcrete examples 1 to 4.

Similar to the mode-locked solid-state laser apparatus of FIG. 1, themode-locked solid-state laser apparatus of FIG. 17 is also small insize, can be manufactured at low cost, can stably operate, and canrealize continuous-wave (CW) mode locking by which pulses having a pulsewidth on the order of femtoseconds are generated.

1. A mode-locked solid-state laser apparatus comprising: a resonatorhaving an output mirror at one end of the resonator; a solid-state lasermedium arranged in said resonator; and a saturable absorbing mirrorarranged in said resonator; wherein said solid-state laser medium isarranged at a distance equal to or smaller than twice the Rayleigh rangefrom said saturable absorbing mirror; said saturable absorbing mirrorhas a depth of absorbing modulation equal to or greater than 0.4%; saidmode-locked solid-state laser apparatus is configured to impart a totalintracavity dispersion D to light having a predetermined wavelengthduring a round trip of the light in said resonator, where the totalintracavity dispersion D is smaller than zero and makes the light havesuch a pulse bandwidth that said saturable absorbing mirror can suppressoperational modes other than operational modes generating soliton pulsesrepeated with a fundamental repetition period, and the absolute value|D| of the total intracavity dispersion D has a relationship expressedby an equation,${\tau_{P} = {\frac{1.76{D}\lambda_{0}A_{{eff},L}}{4\; \pi \; n_{2}l_{S}}\frac{1}{E_{P}}}},$with a pulse width τ_(P) and a central wavelength λ₀ of the light, abeam cross section A_(eff,L) of the light in the solid-state lasermedium, a nonlinear refractive index n₂ and a crystal length l_(S) ofthe solid-state laser medium, pulse energy E_(p) in said resonator; andsaid output mirror is a negative-dispersion mirror which has adielectric multilayer structure being formed on a substrate andincluding two multilayer mirrors and a cavity layer, which is sandwichedbetween the two multilayer mirrors and causes resonance of the lightbetween the two multilayer mirrors, and the negative-dispersion mirrorcauses a mirror dispersion of −3000 fsec² to −600 fsec² in the lighthaving said predetermined wavelength and realizes a reflectance of 97%to 99.5% at the predetermined wavelength.
 2. A mode-locked solid-statelaser apparatus according to claim 1, wherein said resonator has anoptical axis, and includes a dichroic mirror which transmits said lightand is arranged on the optical axis or on an extension of the opticalaxis so that when excitation light for exciting the solid-state lasermedium is injected into said resonator along a direction nonparallel tothe optical axis, the excitation light is reflected by the dichroicmirror and propagates along the optical axis.
 3. A mode-lockedsolid-state laser apparatus according to claim 1, wherein saidsolid-state laser medium is doped with a rare-earth element.
 4. Amode-locked solid-state laser apparatus according to claim 3, whereinsaid rare-earth element is at least one of ytterbium (Yb), erbium (Er),and neodymium (Nd).
 5. A mode-locked solid-state laser apparatusaccording to claim 3, wherein said solid-state laser medium is one ofYb:YAG (Y₃Al₅O₁₂), Yb:KYW (KY(WO₄)₂), Yb:KGW (KGd(WO₄)₂), Yb:Y₂O₃,Yb:Sc₂O₃, Yb:Lu₂O₃, Er,Yb:glass, and Nd:glass.
 6. A mode-lockedsolid-state laser apparatus according to claim 1, wherein said resonatoris a linear resonator.
 7. A mode-locked solid-state laser apparatusaccording to claim 1, wherein said light has a mode diameter of 100micrometers or smaller at a waist when the light is oscillated in theresonator.
 8. A mode-locked solid-state laser apparatus according toclaim 1, wherein said substrate of said negative-dispersion mirror has aconcave surface, and said dielectric multilayer structure is arranged atthe concave surface.
 9. A mode-locked solid-state laser apparatusaccording to claim 1, wherein said negative-dispersion mirror causessaid mirror dispersion of −3000 fsec² to −600 fsec² and realizes saidreflectance of 97% to 99.5% in a wavelength range containing saidpredetermined wavelength and having a bandwidth equal to or greater than10 nm.
 10. A mode-locked solid-state laser apparatus according to claim1, wherein said predetermined wavelength is in a wavelength range of1000 nm to 1100 nm.
 11. A mode-locked solid-state laser apparatusaccording to claim 1, wherein said cavity layer in saidnegative-dispersion mirror has an optical thickness equal to or greaterthan half of said predetermined wavelength.
 12. A mode-lockedsolid-state laser apparatus according to claim 1, wherein each of layersconstituting said two multilayer mirrors in said negative-dispersionmirror has an optical thickness equal to or greater than one-eighth ofsaid predetermined wavelength and smaller than half of the predeterminedwavelength.
 13. A mode-locked solid-state laser apparatus according toclaim 1, wherein said two multilayer mirrors in said negative-dispersionmirror are each constituted by high-index layers having relatively highrefractive indexes and low-index layers having relatively low refractiveindexes which are alternately laminated, and the total number of thehigh-index layers and the low-index layers in each of the two multilayermirrors is eight or greater.
 14. A mode-locked solid-state laserapparatus according to claim 13, wherein said cavity layer in saidnegative-dispersion mirror is formed of an identical material to one ofsaid high-index layers and said low-index layers.
 15. A mode-lockedsolid-state laser apparatus according to claim 13, wherein saidhigh-index layers in said negative-dispersion mirror are formed of oneof a sulfide of Zn and oxides of Ti, Zr, Hf, Nb, Al, Zn, Y, Sc, La, Ce,Pr, and Ta, or a compound or mixture containing one or a combination ofa sulfide of Zn and oxides of Ti, Zr, Hf, Nb, Al, Zn, Y, Sc, La, Ce, Pr,and Ta.
 16. A mode-locked solid-state laser apparatus according to claim13, wherein said low-index layers in said negative-dispersion mirror areformed of one of an oxide of Si and fluorides of Ca, Li, Mg, Na, Th, Al,Hf, La, Y, and Zr, or a compound or mixture containing one or acombination of an oxide of Si and fluorides of Ca, Li, Mg, Na, Th, Al,Hf, La, Y, and Zr.